THEORETICAL CALCULATIONS OF THR GAMMA RADIATION SPECTRUM, ETC.
THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD
distribution of photons according to both energy and direction as a function of position in
spectrum received from all directions 1,000
yards distant from a source of 2 million electron
Extensive recent calculations have been made
with this equation using the method of moments
as developed by Spencer and Fano {1}, wherein
taken as arbitrary units of energy, the shape of
this spectrum shows that at 1,000 yards much
of the gamma energyhas already been degraded
to legs than the 2 Mev source energy.
These same conclusions can be expressed also
the transporting medium; and the equation can
be set-up for several source geomotries of interest [2].
the flux function of the transport equation is
expandedinto 2 series of Legendre polynomials.
The first few of aseries of linked integral equa-
tions related to these polynomials have been
solved numerically on the NBS “SEAC”’ caleu-
Jator for gamma sources of various initial energies in various media, From these solutions,
in turn, differential spherical or so-called 4x
energy spectra and integral energy or dose
spectra at different distances from the source
have been obtained. Then by superposition of
solutions, spectra have been determined from
sources composed of more than one energy.
Details of this method, its solution, and its
application have been reviewed in unclassified
AFSWPdocument 502-A [2].
APPLICATION
The application of this gamma ray transport
equation and its solutions to bomb radiations
has been dealt with most satisfactorily for the
initial gamma radiation.
Herathe problem resolves itself into the deter-
mination of the proper source input data for the
transport equation when all that is known about
the bomb a priori is its presumptive yield plus
certain parameters relating to its nuclear fuel
composition and internal geometry.
The important gamma radiation sources from
bombsare the cloud of radioactive fission prod-
ucts and the radiative capture of bomb neutrons
in external materials, particularly nitrogen of
the surrounding air. These sources are often
referred to as the fission product gammas and
the nitrogen capture gammas, respectively.
The general theoretical treatment of gamma
photon propagation from an effective point
source in air takes the form shown in Figure 1.
This figure shows
the differential energy
4l
ia
9
volts, that is: 2 Mev, gamma photens in air.
Although the units along the ordinate may be
by an integral energy spectrum; or after conversion to air dose by proper consideration of
the true coefficientof absorption of air as a func-
tion of photon energy, they may also be expressed by an integral dose spectrum, as seen in
Figure 2. In this case the ordinate represents
the fraction of total energy or dose delivered by
photons whose energyis less than a given value,
as indicated by the abscissa,
For example:
1,000 yards awayfrom a 2 Mev gammasource,
Pt,a) cio?
40
one-half the air dosois delivered by photons of
energy less than 1 Mev.
Figure 3 presents the differential energy spectrum of the same 2 Mev source, nowseen from
3,000 yards away. Compared with the spectrumi at 1,000 yards (fig. 1), even further degradation has oceurred——due mostly to Compton
scattering events. Thus the unattenuated 2
Mev source photons are relatively even less
prominent at 3,000 yards from the source.
By exiending solutions of this type to a num-
ber of different source energies at. several dis-
tances, interpolation curves can be drawn up,
plotting fraction of dose delivered by photons
of a given energy against source energy.
Figure 4 shows an example of interpolation
curves at 1,000 yards from a point isotropic
source, For example: For a gamma source
component of 6 Mev, 35 percent of the dose at
1,000 yardsis delivered by photons of 4 Mev or
less, 56 percent, by scattered photons of all
energies, and the remainder by unscattered 6
Mevphotons. Suchinterpolation curves enable
the preparation of crude dose spectra for arbitrary source energies,
In Figure 5 are similar interpolation curves
for 1,500 yards. One can see that for any given
source component the fraction of dose delivered
by scattered photons or by photons up to any
ENERGY (Mev)
FraurE 1.—~-Point isotropic source, differential energy spectrumat 1,000 yards, Ho-= 2 Mev.
given energy increases with increasing distance.
This is also suggested by the differential dose
spectra for a monocnergetic 2 Mev source seen
in Figures 1 and 3.
In Figure 6, finally, are interpolation curves
at 3,000 yards. At this distance even the
very most energetie gamma sources deliver
most of their dcs2 through scattered photons.
For example: even for a 10 Mev source component, 66 percent of the dose derives from.
scattered photons, compared with a comparable
figure of 41 percent at 1,000 yards. In common technical jargon the dose build-up factor
is defined as the total dose delivered by all
photons derived from source photons of a given
energy, divided by the dose delivered by un-